ECS455: Chapter 5 OFDM. ECS455: Chapter 5 OFDM. OFDM: Overview. OFDM Applications. Dr.Prapun Suksompong prapun.com/ecs455
|
|
- Ellen Perkins
- 5 years ago
- Views:
Transcription
1 ECS455: Chapter 5 OFDM OFDM: Overview Let S = (S 1, S 2,, S ) contains the information symbols. S IFFT FFT Inverse fast Fourier transform Fast Fourier transform 1 Dr.Prapun Suksompong prapun.com/ecs455 Office Hours: BKD, 6th floor of Sirindhralai building Tuesday 14:20-15:20 Wednesday 14:20-15:20 Friday 9:15-10:15 4 OFDM Applications Wi-Fi: a/g/n/ac versions DVB-T (Digital Video Broadcasting Terrestrial) terrestrial digital TV broadcast system used in most of the world outside orth America DMT (the standard form of ADSL - Asymmetric Digital Subscriber Line) WiMAX, LTE (OFDMA) xf xf xf xf X X X X X F X F X F X F ECS455: Chapter 5 OFDM X X X X 5.1 Implementation: DFT and FFT 2 5 Dr.Prapun Suksompong prapun.com/ecs455 Office Hours: BKD, 6th floor of Sirindhralai building Tuesday 14:20-15:20 Wednesday 14:20-15:20 Friday 9:15-10:15
2 OFDM and CDMA CDMA s key equation All the rows of are orthogonal Key property of : For sync. CDMA, we use the Hadamard matrix H. For OFDM, we use DFT matrix. The matrix is complex-valued. DFT matrix Key Property: Element on the pth row and qth column is given by j p q e ote that the -1 are there because we start from row 1 and column 1 (not from row 0 and column 0). 7 9 Discrete Fourier Transform (DFT) Here, we work with -point signals (finite-length sequences (vectors) of length ) in both time and frequency domain. Example: = 2 8 x X x X x X 10 Suppose >> fft([2 5]) ans = 7-3 >> ifft([7-3]) ans = 2 5
3 Connection to CDMA Efficient Implementation: (I)FFT The rows of are orthogonal. So are the columns. Proof: Let be the k th row of. k k kq kq k q k q q q q q kk kk q q 11 kk j e kk kk kk kk k k q k k q So, replaces the role of in CDMA. 13 [Bahai, 2002, Fig. 2.9] An -point FFT requires only on the order of log multiplications, rather than 2 as in a straightforward computation. Discrete Fourier Transform (DFT) Matrix form: Pointwise form: n k or, equivalently, nk X k x n X k x n n k j ft j ft xt X f e df x f X te dt 12 n jnk X k e x n X k x n e Comparison with Fourier transform n k n nk jnk 14 FFT The history of the FFT is complicated. As with many discoveries and inventions, it arrived before the (computer) world was ready for it. Usually done with a power of two. Very efficient in terms of computing time Ideally suited to the binary arithmetic of digital computers. Ex: From the implementation point of view it is better to have, for example, a FFT size of 1024 even if only 600 outputs are used than try to have another length for FFT between 600 and References: E. Oran Brigham, The Fast Fourier Transform, Prentice-Hall, 1974.
4 OFDM with Memoryless Channel 15 Sample every T s / ht t h t t rt ht st wt st wt rn sn wn FFT sn S n R n S W k k k Additive white Gaussian noise Sub-channel are independent. (o ICI) 17 ECS455: Chapter 5 OFDM Dr.Prapun Suksompong prapun.com/ecs Cyclic Prefix (CP) OFDM implementation by IFFT/FFT S k Multipath Propagation In a wireless mobile communication system, a transmitted signal propagating through the wireless channel often encounters multiple reflective paths until it reaches the receiver We refer to this phenomenon as multipath propagation and it causes fluctuation of the amplitude and phase of the received signal. We call this fluctuation multipath fading. R k S k 16 This form of OFDM is often referred to as Discrete Multi-Tone (DMT). 18
5 Cyclic Prefix: Motivation To reduce the ISI, add guard interval larger than that of the estimated delay spread. If the guard interval is left empty, multipath fading will destroy orthogonality of the sub-carriers, i.e., ICI (inter-channel interference) still exists. Solution: To prevent both the ISI as well as the ICI, OFDM symbol is cyclically extended into the guard interval. Cyclic Prefix Channel with Finite Memory Discrete time baseband model: Remarks: y n h s n w n h m s n m w n where iid v m hn nn C wn We will assume that [Tse Viswanath, 2005, Sec ] Recall: Convolution Flip Shift Multiply (pointwise) Add x hn xmhnm m 20 22
6 23 Circular Convolution Replicate x (now it looks periodic) Then, perform the usual convolution only from n = 0 to -1 (Regular Convolution) 25 Discussion Regular convolution of an 1 point vector and an 2 point vector gives ( )-point vector. Circular convolution is performed between two equallength vectors. The results also has the same length. Circular convolution can be used to find regular convolution by zero-padding. Zero-pad the vectors so that their length is Example: 24 Circular Convolution: Examples 1 Find >> conv([1,2,3],[4,5,6]) ans = >> cconv([1,2,3],[4,5,6],3) ans = >> cconv([1,2,3,0,0],[4,5,6,0,0],5) ans = Circular Convolution in Communication We want the receiver to obtain the circular convolution of the signal (channel input) and the channel. Q: Why? A: CTFT: convolution in time domain corresponds to multiplication in frequency domain. This fact does not hold for DFT. DFT: circular convolution in (discrete) time domain corresponds to multiplication in (discrete) frequency domain. We want to have multiplication in frequency domain. So, we want circular convolution and not the regular convolution. Problem: Real channel does regular convolution. Solution: With cyclic prefix, regular convolution can be used to create circular convolution.
7 Let s look closer at how we carry out the circular Example 2 convolution operation. Recall that we replicate the x and then perform the Solution: regular convolution (for points) Example 2 Copy the last samples of the symbols to the beginning of the symbol. This partial replica is called the cyclic prefix. Try this: use only the necessary part of the replica and then convolute (regular convolution) with the channel. 27 Goal: Get these numbers using regular convolution 29 Junk! Example 2 Observation: We don t need to replicate the x indefinitely. Furthermore, when h is shorter than x, we need only a part of one replica. ot needed in the calculation Example 2 We now know that Cyclic Prefix Similarly, you may check that Cyclic Prefix 28 30
8 Example 3 We know, from Example 2, that [ ] * [3 2 1] = [ ] And that [ ] * [3 2 1] = [ ] Check that [ ] * [3 2 1] = [ ] and [ ] * [3 2 1] Putting results together Suppose x (1) = [ ] and x (2) = [ ] Suppose h = [3 2 1] At the receiver, we want to get [ ] * [ ] = [ ] [ ] * [ ] = [ ] We transmit [ ]. Cyclic prefix Cyclic prefix At the receiver, we get [ ] * [3 2 1] = [ ] = [ ] Junk! To be thrown away by the receiver. Example 4 We know that [ ] * [3 2 1] = [ ] [ ] * [3 2 1] = [ ] Using Example 3, we have [ ] * [3 2 1] = [ ] * [3 2 1] +[ ] = [ ] +[ ] = [ ] Circular Convolution: Key Properties Consider an -point signal x[n] Cyclic Prefix (CP) insertion: If x[n] is extended by copying the last samples of the symbols at the beginning of the symbol: Key Property 1: Key Property 2: xn n xn xn vn h x n hx n n h x n H X k k 32 34
9 35 h h h h OFDM with CP for Channel w/ Memory To send samples S = (S 0, S 1,, S -1 ) First apply IFFT with scaling by : Then, add cyclic prefix s s s s This is inputted to the channel The channel output is which can be viewed as p p r r Remove cyclic prefix to get. (We know that.) Then apply FFT with scaling by : By circular convolution property of DFT, R HS k k k R zero-padded to length HS k k k Rk Sk H k o ICI! 37 MATLAB Example (2/2) % % Convolve with channel y = i i i i i y = conv(x,h); i i i i i H = fft([h zeros(1,-v-1)]); i i % % OFDM receiver y = y(1:((+v)*n)); yt = reshape(y,(+v),n).'; % Reshape matrix for easier % removal of cyclic prefix r = yt(:,v+1:v+); % Eliminate junk (cyclic prefix) Rt = (1/sqrt())*fft(r,[],2); % Calculate the FFT with scaling r = i i i i FFT Rt = i i i i w/ scaling i i i i i i i i (row-wise) % "Equalization" S_hatt = zeros(size(rt)); for i=1:length(h) S_hatt(:,i) = Rt(:,i)/H(i); end S_hat = reshape(s_hatt.',1,*n) % Divide Rk (the kth column) by Hk Shatt = S_hat = [ ] MATLAB Example (1/2) S = [ ]; % data stream h = [ ]; % OFDM transmitter = 4; % umber of data symbols per OFDM symbol n = length(s)/; % umber of data blocks St = (reshape(s,,n)).'; % Reshape stream to matrix for % easier addition of cyclic prefix st = (sqrt())*ifft(st,[],2); % Calculate the IFFT with scaling St = IFFT w/ scaling (row-wise) st = i i c i i i i i i v = length(h)-1; xt = [st(:,(-(v-1)):) st]; % Add Cyclic Prefix x = (reshape(xt.',((+v)*n),1)).'; % Reshape back to stream OFDM System Design: CP A good ratio between the CP interval and symbol duration should be found, so that all multipaths are resolved and not significant amount of energy is lost due to CP. As a thumb rule, the CP interval must be two to four times larger than the root mean square (RMS) delay spread. x = i i i i i i i i i i i i [Tarokh, 2009, Fig 2.9]
10 Summary The CP at the beginning of each block has two main functions. As guard interval, it prevents contamination of a block by ISI from the previous block. It makes the received block appear to be periodic of period. Turn regular convolution into circular convolution Point-wise multiplication in the frequency domain Reference A. Bahai, B. R. Saltzberg, and M. Ergen, Multi-Carrier Digital Communications: Theory and Applications of OFDM, 2nd ed., ew York: Springer Verlag, OFDM Architecture 40 [Bahai, 2002, Fig 1.11]
ECS455: Chapter 5 OFDM
ECS455: Chapter 5 OFDM 5.4 Cyclic Prefix (CP) 1 Dr.Prapun Suksopong prapun.co/ecs455 Office Hours: BKD 3601-7 Tuesday 9:30-10:30 Friday 14:00-16:00 Three steps towards odern OFDM 1. Mitigate Multipath
More informationEE6604 Personal & Mobile Communications. Week 15. OFDM on AWGN and ISI Channels
EE6604 Personal & Mobile Communications Week 15 OFDM on AWGN and ISI Channels 1 { x k } x 0 x 1 x x x N- 2 N- 1 IDFT X X X X 0 1 N- 2 N- 1 { X n } insert guard { g X n } g X I n { } D/A ~ si ( t) X g X
More informationMobile Communications TCS 455
Mobile Counication TCS 455 Dr. Prapun Sukopong prapun@iit.tu.ac.th Lecture 24 1 Office Hour: BKD 3601-7 Tueday 14:00-16:00 Thurday 9:30-11:30 Announceent Read Chapter 9: 9.1 9.5 Section 1.2 fro [Bahai,
More informationNagoya Institute of Technology
09.03.19 1 2 OFDM SC-FDE (single carrier-fde)ofdm PAPR 3 OFDM SC-FDE (single carrier-fde)ofdm PAPR 4 5 Mobility 2G GSM PDC PHS 3G WCDMA cdma2000 WLAN IEEE802.11b 4G 20112013 WLAN IEEE802.11g, n BWA 10kbps
More informationECS455: Chapter 4 Multiple Access
ECS455: Chapter 4 Multiple Access 4.4 m-sequence Binary Random Sequence X -4 X -3 X -2 X - X -0 X X 2 X 3 X 4 Coin-flipping sequence H H T H H T H T T Bernoullitrials/sequence 0 0 0 0 Binary (indp.) random
More informationDFT-Based FIR Filtering. See Porat s Book: 4.7, 5.6
DFT-Based FIR Filtering See Porat s Book: 4.7, 5.6 1 Motivation: DTFT View of Filtering There are two views of filtering: * Time Domain * Frequency Domain x[ X f ( θ ) h[ H f ( θ ) Y y[ = h[ * x[ f ( θ
More informationEEO 401 Digital Signal Processing Prof. Mark Fowler
EEO 401 Digital Signal Processing Prof. Mark Fowler Note Set #21 Using the DFT to Implement FIR Filters Reading Assignment: Sect. 7.3 of Proakis & Manolakis Motivation: DTFT View of Filtering There are
More informationECS455: Chapter 4 Multiple Access
ECS455: Chapter 4 Multiple Access 4.4 m-sequence 25 Dr.Prapun Suksompong prapun.com/ecs455 Office Hours: BKD, 6th floor of Sirindhralai building Tuesday 14:20-15:20 Wednesday 14:20-15:20 Friday 9:15-10:15
More informationECS455 Chapter 3 Call Blocking Probability
ECS455 Chapter 3 Call Blocking Probability 1 Dr.Prapun Suksompong prapun.com/ecs455 Office Hours: BKD, 6th floor of Sirindhralai building Tuesday 14:20-15:20 Wednesday 14:20-15:20 Friday 9:15-10:15 Introduction
More informationSingle-Carrier Block Transmission With Frequency-Domain Equalisation
ELEC6014 RCNSs: Additional Topic Notes Single-Carrier Block Transmission With Frequency-Domain Equalisation Professor Sheng Chen School of Electronics and Computer Science University of Southampton Southampton
More informationLecture 8: Orthogonal Frequency Division Multiplexing (OFDM)
Communication Systems Lab Spring 2017 ational Taiwan University Lecture 8: Orthogonal Frequency Division Multiplexing (OFDM) Scribe: 謝秉昂 陳心如 Lecture Date: 4/26, 2017 Lecturer: I-Hsiang Wang 1 Outline 1
More informationIn this Lecture. Frequency domain analysis
In this Lecture Frequency domain analysis Introduction In most cases we want to know the frequency content of our signal Why? Most popular analysis in frequency domain is based on work of Joseph Fourier
More informationAnalog vs. discrete signals
Analog vs. discrete signals Continuous-time signals are also known as analog signals because their amplitude is analogous (i.e., proportional) to the physical quantity they represent. Discrete-time signals
More informationA Computationally Efficient Block Transmission Scheme Based on Approximated Cholesky Factors
A Computationally Efficient Block Transmission Scheme Based on Approximated Cholesky Factors C. Vincent Sinn Telecommunications Laboratory University of Sydney, Australia cvsinn@ee.usyd.edu.au Daniel Bielefeld
More informationFBMC/OQAM transceivers for 5G mobile communication systems. François Rottenberg
FBMC/OQAM transceivers for 5G mobile communication systems François Rottenberg Modulation Wikipedia definition: Process of varying one or more properties of a periodic waveform, called the carrier signal,
More informationCommunications and Signal Processing Spring 2017 MSE Exam
Communications and Signal Processing Spring 2017 MSE Exam Please obtain your Test ID from the following table. You must write your Test ID and name on each of the pages of this exam. A page with missing
More informationLecture 4 Capacity of Wireless Channels
Lecture 4 Capacity of Wireless Channels I-Hsiang Wang ihwang@ntu.edu.tw 3/0, 014 What we have learned So far: looked at specific schemes and techniques Lecture : point-to-point wireless channel - Diversity:
More informationLecture 7: Wireless Channels and Diversity Advanced Digital Communications (EQ2410) 1
Wireless : Wireless Advanced Digital Communications (EQ2410) 1 Thursday, Feb. 11, 2016 10:00-12:00, B24 1 Textbook: U. Madhow, Fundamentals of Digital Communications, 2008 1 / 15 Wireless Lecture 1-6 Equalization
More informationEstimation of the Capacity of Multipath Infrared Channels
Estimation of the Capacity of Multipath Infrared Channels Jeffrey B. Carruthers Department of Electrical and Computer Engineering Boston University jbc@bu.edu Sachin Padma Department of Electrical and
More informationPhysical Layer and Coding
Physical Layer and Coding Muriel Médard Professor EECS Overview A variety of physical media: copper, free space, optical fiber Unified way of addressing signals at the input and the output of these media:
More informationModule 3. Convolution. Aim
Module Convolution Digital Signal Processing. Slide 4. Aim How to perform convolution in real-time systems efficiently? Is convolution in time domain equivalent to multiplication of the transformed sequence?
More informationFall 2011, EE123 Digital Signal Processing
Lecture 6 Miki Lustig, UCB September 11, 2012 Miki Lustig, UCB DFT and Sampling the DTFT X (e jω ) = e j4ω sin2 (5ω/2) sin 2 (ω/2) 5 x[n] 25 X(e jω ) 4 20 3 15 2 1 0 10 5 1 0 5 10 15 n 0 0 2 4 6 ω 5 reconstructed
More informationLarge Zero Autocorrelation Zone of Golay Sequences and 4 q -QAM Golay Complementary Sequences
Large Zero Autocorrelation Zone of Golay Sequences and 4 q -QAM Golay Complementary Sequences Guang Gong 1 Fei Huo 1 and Yang Yang 2,3 1 Department of Electrical and Computer Engineering University of
More informationMulticarrier transmission DMT/OFDM
W. Henkel, International University Bremen 1 Multicarrier transmission DMT/OFDM DMT: Discrete Multitone (wireline, baseband) OFDM: Orthogonal Frequency Division Multiplex (wireless, with carrier, passband)
More informationLecture 2. Fading Channel
1 Lecture 2. Fading Channel Characteristics of Fading Channels Modeling of Fading Channels Discrete-time Input/Output Model 2 Radio Propagation in Free Space Speed: c = 299,792,458 m/s Isotropic Received
More informationHST.582J / 6.555J / J Biomedical Signal and Image Processing Spring 2007
MIT OpenCourseare http://ocw.mit.edu HST.58J / 6.555J / 16.56J Biomedical Signal and Image Processing Spring 7 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
More informationSquare Root Raised Cosine Filter
Wireless Information Transmission System Lab. Square Root Raised Cosine Filter Institute of Communications Engineering National Sun Yat-sen University Introduction We consider the problem of signal design
More informationDiscrete Fourier Transform
Discrete Fourier Transform Virtually all practical signals have finite length (e.g., sensor data, audio records, digital images, stock values, etc). Rather than considering such signals to be zero-padded
More informationENT 315 Medical Signal Processing CHAPTER 2 DISCRETE FOURIER TRANSFORM. Dr. Lim Chee Chin
ENT 315 Medical Signal Processing CHAPTER 2 DISCRETE FOURIER TRANSFORM Dr. Lim Chee Chin Outline Introduction Discrete Fourier Series Properties of Discrete Fourier Series Time domain aliasing due to frequency
More informationLecture 8: MIMO Architectures (II) Theoretical Foundations of Wireless Communications 1. Overview. Ragnar Thobaben CommTh/EES/KTH
MIMO : MIMO Theoretical Foundations of Wireless Communications 1 Wednesday, May 25, 2016 09:15-12:00, SIP 1 Textbook: D. Tse and P. Viswanath, Fundamentals of Wireless Communication 1 / 20 Overview MIMO
More informationDigital Communication Systems ECS 452
Digital Communication Systems ECS 452 Asst. Prof. Dr. Prapun Suksompong prapun@siit.tu.ac.th 3 Discrete Memoryless Channel (DMC) Office Hours: BKD, 6th floor of Sirindhralai building Tuesday 4:20-5:20
More informationPrinciples of Communications Lecture 8: Baseband Communication Systems. Chih-Wei Liu 劉志尉 National Chiao Tung University
Principles of Communications Lecture 8: Baseband Communication Systems Chih-Wei Liu 劉志尉 National Chiao Tung University cwliu@twins.ee.nctu.edu.tw Outlines Introduction Line codes Effects of filtering Pulse
More informationIntercarrier and Intersymbol Interference Analysis of OFDM Systems on Time-Varying channels
Intercarrier and Intersymbol Interference Analysis of OFDM Systems on Time-Varying channels Van Duc Nguyen, Hans-Peter Kuchenbecker University of Hannover, Institut für Allgemeine Nachrichtentechnik Appelstr.
More informationIntroduction to DFT. Deployment of Telecommunication Infrastructures. Azadeh Faridi DTIC UPF, Spring 2009
Introduction to DFT Deployment of Telecommunication Infrastructures Azadeh Faridi DTIC UPF, Spring 2009 1 Review of Fourier Transform Many signals can be represented by a fourier integral of the following
More informationEE5713 : Advanced Digital Communications
EE5713 : Advanced Digital Communications Week 12, 13: Inter Symbol Interference (ISI) Nyquist Criteria for ISI Pulse Shaping and Raised-Cosine Filter Eye Pattern Equalization (On Board) 20-May-15 Muhammad
More informationFourier Analysis of Signals Using the DFT
Fourier Analysis of Signals Using the DFT ECE 535 Lecture April 29, 23 Overview: Motivation Many applications require analyzing the frequency content of signals Speech processing study resonances of vocal
More informationLecture 6: Modeling of MIMO Channels Theoretical Foundations of Wireless Communications 1. Overview. CommTh/EES/KTH
: Theoretical Foundations of Wireless Communications 1 Wednesday, May 11, 2016 9:00-12:00, Conference Room SIP 1 Textbook: D. Tse and P. Viswanath, Fundamentals of Wireless Communication 1 / 1 Overview
More informationEE123 Digital Signal Processing
Announcements EE Digital Signal Processing otes posted HW due Friday SDR give away Today! Read Ch 9 $$$ give me your names Lecture based on slides by JM Kahn M Lustig, EECS UC Berkeley M Lustig, EECS UC
More informationCopyright license. Exchanging Information with the Stars. The goal. Some challenges
Copyright license Exchanging Information with the Stars David G Messerschmitt Department of Electrical Engineering and Computer Sciences University of California at Berkeley messer@eecs.berkeley.edu Talk
More informationLECTURE 16 AND 17. Digital signaling on frequency selective fading channels. Notes Prepared by: Abhishek Sood
ECE559:WIRELESS COMMUNICATION TECHNOLOGIES LECTURE 16 AND 17 Digital signaling on frequency selective fading channels 1 OUTLINE Notes Prepared by: Abhishek Sood In section 2 we discuss the receiver design
More information8 The Discrete Fourier Transform (DFT)
8 The Discrete Fourier Transform (DFT) ² Discrete-Time Fourier Transform and Z-transform are de ned over in niteduration sequence. Both transforms are functions of continuous variables (ω and z). For nite-duration
More informationECS332: Midterm Examination (Set I) Seat
Sirindhorn International Institute of Technology Thammasat University at Rangsit School of Information, Computer and Communication Technology ECS33: Midterm Examination (Set I) COURSE : ECS33 (Principles
More informationLecture 5: Antenna Diversity and MIMO Capacity Theoretical Foundations of Wireless Communications 1. Overview. CommTh/EES/KTH
: Antenna Diversity and Theoretical Foundations of Wireless Communications Wednesday, May 4, 206 9:00-2:00, Conference Room SIP Textbook: D. Tse and P. Viswanath, Fundamentals of Wireless Communication
More information13.1 Convolution and Deconvolution Using the FFT
538 Chapter 13. Fourier and Spectral Applications 13.1 Convolution and Deconvolution Using the FFT We have defined the convolution of two functions for the continuous case in equation (12..8), and have
More informationIntroduction to Sparsity in Signal Processing
1 Introduction to Sparsity in Signal Processing Ivan Selesnick Polytechnic Institute of New York University Brooklyn, New York selesi@poly.edu 212 2 Under-determined linear equations Consider a system
More informationCS 179: GPU Programming. Lecture 9 / Homework 3
CS 179: GPU Programming Lecture 9 / Homework 3 Recap Some algorithms are less obviously parallelizable : Reduction Sorts FFT (and certain recursive algorithms) Parallel FFT structure (radix-2) Bit-reversed
More informationCS6304 / Analog and Digital Communication UNIT IV - SOURCE AND ERROR CONTROL CODING PART A 1. What is the use of error control coding? The main use of error control coding is to reduce the overall probability
More informationLecture 6: Modeling of MIMO Channels Theoretical Foundations of Wireless Communications 1
Fading : Theoretical Foundations of Wireless Communications 1 Thursday, May 3, 2018 9:30-12:00, Conference Room SIP 1 Textbook: D. Tse and P. Viswanath, Fundamentals of Wireless Communication 1 / 23 Overview
More informationFourier Analysis Overview (0B)
CTFS: Continuous Time Fourier Series CTFT: Continuous Time Fourier Transform DTFS: Fourier Series DTFT: Fourier Transform DFT: Discrete Fourier Transform Copyright (c) 2009-2016 Young W. Lim. Permission
More informationEE538 Digital Signal Processing I Session 13 Exam 1 Live: Wed., Sept. 18, Cover Sheet
EE538 Digital Signal Processing I Session 3 Exam Live: Wed., Sept. 8, 00 Cover Sheet Test Duration: 50 minutes. Coverage: Sessions -0. Open Book but Closed Notes. Calculators not allowed. This test contains
More information! Circular Convolution. " Linear convolution with circular convolution. ! Discrete Fourier Transform. " Linear convolution through circular
Previously ESE 531: Digital Signal Processing Lec 22: April 18, 2017 Fast Fourier Transform (con t)! Circular Convolution " Linear convolution with circular convolution! Discrete Fourier Transform " Linear
More informationELECTRONICS & COMMUNICATIONS DIGITAL COMMUNICATIONS
EC 32 (CR) Total No. of Questions :09] [Total No. of Pages : 02 III/IV B.Tech. DEGREE EXAMINATIONS, APRIL/MAY- 207 Second Semester ELECTRONICS & COMMUNICATIONS DIGITAL COMMUNICATIONS Time: Three Hours
More informationECE538 Final Exam Fall 2017 Digital Signal Processing I 14 December Cover Sheet
ECE58 Final Exam Fall 7 Digital Signal Processing I December 7 Cover Sheet Test Duration: hours. Open Book but Closed Notes. Three double-sided 8.5 x crib sheets allowed This test contains five problems.
More informationCS 179: GPU Programming. Lecture 9 / Homework 3
CS 179: GPU Programming Lecture 9 / Homework 3 Recap Some algorithms are less obviously parallelizable : Reduction Sorts FFT (and certain recursive algorithms) Parallel FFT structure (radix-2) Bit-reversed
More informationRandom Matrices and Wireless Communications
Random Matrices and Wireless Communications Jamie Evans Centre for Ultra-Broadband Information Networks (CUBIN) Department of Electrical and Electronic Engineering University of Melbourne 3.5 1 3 0.8 2.5
More informationDiscrete-time signals and systems
Discrete-time signals and systems 1 DISCRETE-TIME DYNAMICAL SYSTEMS x(t) G y(t) Linear system: Output y(n) is a linear function of the inputs sequence: y(n) = k= h(k)x(n k) h(k): impulse response of the
More informationMaximum Achievable Diversity for MIMO-OFDM Systems with Arbitrary. Spatial Correlation
Maximum Achievable Diversity for MIMO-OFDM Systems with Arbitrary Spatial Correlation Ahmed K Sadek, Weifeng Su, and K J Ray Liu Department of Electrical and Computer Engineering, and Institute for Systems
More informationDigital Signal Processing. Midterm 2 Solutions
EE 123 University of California, Berkeley Anant Sahai arch 15, 2007 Digital Signal Processing Instructions idterm 2 Solutions Total time allowed for the exam is 80 minutes Please write your name and SID
More informationLecture 20: Discrete Fourier Transform and FFT
EE518 Digital Signal Processing University of Washington Autumn 2001 Dept of Electrical Engineering Lecture 20: Discrete Fourier Transform and FFT Dec 10, 2001 Prof: J Bilmes TA:
More informationECE6604 PERSONAL & MOBILE COMMUNICATIONS. Week 3. Flat Fading Channels Envelope Distribution Autocorrelation of a Random Process
1 ECE6604 PERSONAL & MOBILE COMMUNICATIONS Week 3 Flat Fading Channels Envelope Distribution Autocorrelation of a Random Process 2 Multipath-Fading Mechanism local scatterers mobile subscriber base station
More informationZF-BLE Joint Detection for TD-SCDMA
ZF-BLE Joint Detection for TD-SCDMA Chengke Sheng Ed Martinez February 19, 2004 Table of Contents 1. INTRODUCTION... 6 1.1. SCOPE AND AUDIENCE... 6 1.2. EXECUTIVE SUMMARY... 6 1.3. BACKGROUND... 6 2. SIGNAL
More informationLECTURE 18. Lecture outline Gaussian channels: parallel colored noise inter-symbol interference general case: multiple inputs and outputs
LECTURE 18 Last time: White Gaussian noise Bandlimited WGN Additive White Gaussian Noise (AWGN) channel Capacity of AWGN channel Application: DS-CDMA systems Spreading Coding theorem Lecture outline Gaussian
More informationChapter 8 The Discrete Fourier Transform
Chapter 8 The Discrete Fourier Transform Introduction Representation of periodic sequences: the discrete Fourier series Properties of the DFS The Fourier transform of periodic signals Sampling the Fourier
More informationFourier analysis of discrete-time signals. (Lathi Chapt. 10 and these slides)
Fourier analysis of discrete-time signals (Lathi Chapt. 10 and these slides) Towards the discrete-time Fourier transform How we will get there? Periodic discrete-time signal representation by Discrete-time
More informationDesign of MMSE Multiuser Detectors using Random Matrix Techniques
Design of MMSE Multiuser Detectors using Random Matrix Techniques Linbo Li and Antonia M Tulino and Sergio Verdú Department of Electrical Engineering Princeton University Princeton, New Jersey 08544 Email:
More informationLecture 4 Capacity of Wireless Channels
Lecture 4 Capacity of Wireless Channels I-Hsiang Wang ihwang@ntu.edu.tw 3/0, 014 What we have learned So far: looked at specific schemes and techniques Lecture : point-to-point wireless channel - Diversity:
More informationRevision of Lecture 4
Revision of Lecture 4 We have completed studying digital sources from information theory viewpoint We have learnt all fundamental principles for source coding, provided by information theory Practical
More informationOFDM Transmission. over Rapidly Changing Channels. Zijian Tang
OFDM Transmission over Rapidly Changing Channels Zijian Tang OFDM Transmission over Rapidly Changing Channels PROEFSCHRIFT ter verkrijging van de graad van doctor aan de Technische Universiteit Delft,
More information2. Wireless Fading Channels
Fundamentals of Wireless Comm. Andreas Biri, D-ITET.07.7. Introduction Modulation (frequency shift to carrier frequency): - enables multiple (slightly shifted) simultaneous channels - better channel characteristics
More informationLecture 7. Fourier Analysis
Lecture 7 Fourier Analysis Summary Lecture 6 Minima and maxima 1 dimension : Bracket minima : 3 values of f(x) : f(2) < f(1) and f(2)
More informationAn Adaptive Blind Channel Shortening Algorithm for MCM Systems
Hacettepe University Department of Electrical and Electronics Engineering An Adaptive Blind Channel Shortening Algorithm for MCM Systems Blind, Adaptive Channel Shortening Equalizer Algorithm which provides
More informationDirect-Sequence Spread-Spectrum
Chapter 3 Direct-Sequence Spread-Spectrum In this chapter we consider direct-sequence spread-spectrum systems. Unlike frequency-hopping, a direct-sequence signal occupies the entire bandwidth continuously.
More informationNeural Networks 2. 2 Receptive fields and dealing with image inputs
CS 446 Machine Learning Fall 2016 Oct 04, 2016 Neural Networks 2 Professor: Dan Roth Scribe: C. Cheng, C. Cervantes Overview Convolutional Neural Networks Recurrent Neural Networks 1 Introduction There
More informationChannel Shortening for Bit Rate Maximization in DMT Communication Systems
Channel Shortening for Bit Rate Maximization in DMT Communication Systems Karima Ragoubi, Maryline Hélard, Matthieu Crussière To cite this version: Karima Ragoubi, Maryline Hélard, Matthieu Crussière Channel
More informationUsing MATLAB with the Convolution Method
ECE 350 Linear Systems I MATLAB Tutorial #5 Using MATLAB with the Convolution Method A linear system with input, x(t), and output, y(t), can be described in terms of its impulse response, h(t). x(t) h(t)
More informationPOWER ALLOCATION AND OPTIMAL TX/RX STRUCTURES FOR MIMO SYSTEMS
POWER ALLOCATION AND OPTIMAL TX/RX STRUCTURES FOR MIMO SYSTEMS R. Cendrillon, O. Rousseaux and M. Moonen SCD/ESAT, Katholiee Universiteit Leuven, Belgium {raphael.cendrillon, olivier.rousseaux, marc.moonen}@esat.uleuven.ac.be
More informationUNIT I INFORMATION THEORY. I k log 2
UNIT I INFORMATION THEORY Claude Shannon 1916-2001 Creator of Information Theory, lays the foundation for implementing logic in digital circuits as part of his Masters Thesis! (1939) and published a paper
More informationProperties of LTI Systems
Properties of LTI Systems Properties of Continuous Time LTI Systems Systems with or without memory: A system is memory less if its output at any time depends only on the value of the input at that same
More informationProjects in Wireless Communication Lecture 1
Projects in Wireless Communication Lecture 1 Fredrik Tufvesson/Fredrik Rusek Department of Electrical and Information Technology Lund University, Sweden Lund, Sept 2018 Outline Introduction to the course
More informationDigital Baseband Systems. Reference: Digital Communications John G. Proakis
Digital Baseband Systems Reference: Digital Communications John G. Proais Baseband Pulse Transmission Baseband digital signals - signals whose spectrum extend down to or near zero frequency. Model of the
More informationNORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY DEPARTMENT OF ELECTRONICS AND TELECOMMUNICATIONS
page 1 of 5 (+ appendix) NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY DEPARTMENT OF ELECTRONICS AND TELECOMMUNICATIONS Contact during examination: Name: Magne H. Johnsen Tel.: 73 59 26 78/930 25 534
More information3.2 Complex Sinusoids and Frequency Response of LTI Systems
3. Introduction. A signal can be represented as a weighted superposition of complex sinusoids. x(t) or x[n]. LTI system: LTI System Output = A weighted superposition of the system response to each complex
More informationSignal Design for Band-Limited Channels
Wireless Information Transmission System Lab. Signal Design for Band-Limited Channels Institute of Communications Engineering National Sun Yat-sen University Introduction We consider the problem of signal
More informationChapter 2 Underwater Acoustic Channel Models
Chapter 2 Underwater Acoustic Channel Models In this chapter, we introduce two prevailing UWA channel models, namely, the empirical UWA channel model and the statistical time-varying UWA channel model,
More informationHomework #1 Solution
February 7, 4 Department of Electrical and Computer Engineering University of Wisconsin Madison ECE 734 VLSI Array Structures for Digital Signal Processing Homework # Solution Due: February 6, 4 in class.
More informationIntroduction to Sparsity in Signal Processing
1 Introduction to Sparsity in Signal Processing Ivan Selesnick Polytechnic Institute of New York University Brooklyn, New York selesi@poly.edu 212 2 Under-determined linear equations Consider a system
More informationMA3232 Summary 5. d y1 dy1. MATLAB has a number of built-in functions for solving stiff systems of ODEs. There are ode15s, ode23s, ode23t, ode23tb.
umerical solutions of higher order ODE We can convert a high order ODE into a system of first order ODEs and then apply RK method to solve it. Stiff ODEs Stiffness is a special problem that can arise in
More informationA6523 Signal Modeling, Statistical Inference and Data Mining in Astrophysics Spring
A653 Signal Modeling, Statistical Inference and Data Mining in Astrophysics Spring 15 http://www.astro.cornell.edu/~cordes/a653 Lecture 3 Power spectrum issues Frequentist approach Bayesian approach (some
More information2013/Fall-Winter Term Monday 12:50 Room# or 5F Meeting Room Instructor: Fire Tom Wada, Professor
SYSTEM ARCHITECTURE ADVANCED SYSTEM ARCHITECTURE Error Correction Code 1 01/Fall-Winter Term Monday 1:50 Room# 1- or 5F Meeting Room Instructor: Fire Tom Wada, Professor 014/1/0 System Arch 1 Introduction
More informationCS6956: Wireless and Mobile Networks Lecture Notes: 2/4/2015
CS6956: Wireless and Mobile Networks Lecture Notes: 2/4/2015 [Most of the material for this lecture has been taken from the Wireless Communications & Networks book by Stallings (2 nd edition).] Effective
More informationMinimum BER Linear Transceivers for Block. Communication Systems. Lecturer: Tom Luo
Minimum BER Linear Transceivers for Block Communication Systems Lecturer: Tom Luo Outline Block-by-block communication Abstract model Applications Current design techniques Minimum BER precoders for zero-forcing
More informationTopic 7. Convolution, Filters, Correlation, Representation. Bryan Pardo, 2008, Northwestern University EECS 352: Machine Perception of Music and Audio
Topic 7 Convolution, Filters, Correlation, Representation Short time Fourier Transform Break signal into windows Calculate DFT of each window The Spectrogram spectrogram(y,1024,512,1024,fs,'yaxis'); A
More informationResidual carrier frequency offset and symbol timing offset in narrow-band OFDM modulation
Residual carrier frequency offset and symbol timing offset in narrow-band OFDM modulation Master s thesis iko Ohukainen 2264750 Department of Mathematical Sciences University of Oulu Spring 2017 Contents
More informationEE-210. Signals and Systems Homework 7 Solutions
EE-20. Signals and Systems Homework 7 Solutions Spring 200 Exercise Due Date th May. Problems Q Let H be the causal system described by the difference equation w[n] = 7 w[n ] 2 2 w[n 2] + x[n ] x[n 2]
More informationNew theoretical framework for OFDM/CDMA systems with peak-limited nonlinearities
Science in China Series F: Information Sciences 7 SCIENCE IN CHINA PRESS Springer New theoretical framewor for OFDM/CDMA systems with pea-limited nonlinearities WANG Jian, ZHANG Lin, SHAN XiuMing & REN
More informationLecture 11 FIR Filters
Lecture 11 FIR Filters Fundamentals of Digital Signal Processing Spring, 2012 Wei-Ta Chu 2012/4/12 1 The Unit Impulse Sequence Any sequence can be represented in this way. The equation is true if k ranges
More informationSignal Model and System Definitions
Chapter 3 Signal Model and System Definitions A general system description and signal model definitions are needed before designing linearization algorithms. Many of the definitions and notations included
More information9 THEORY OF CODES. 9.0 Introduction. 9.1 Noise
9 THEORY OF CODES Chapter 9 Theory of Codes After studying this chapter you should understand what is meant by noise, error detection and correction; be able to find and use the Hamming distance for a
More informationA Family of Nyquist Filters Based on Generalized Raised-Cosine Spectra
Proc. Biennial Symp. Commun. (Kingston, Ont.), pp. 3-35, June 99 A Family of Nyquist Filters Based on Generalized Raised-Cosine Spectra Nader Sheikholeslami Peter Kabal Department of Electrical Engineering
More informationAdvanced 3G and 4G Wireless Communication Prof. Aditya K. Jagannatham Department of Electrical Engineering Indian Institute of Technology, Kanpur
Advanced 3G and 4G Wireless Communication Prof. Aditya K. Jagannatham Department of Electrical Engineering Indian Institute of Technology, Kanpur Lecture - 12 Doppler Spectrum and Jakes Model Welcome to
More information